Quantum Concatenated Code Hamiltonians

随着计算机的基本构建块缩小到原子尺度，新的物理学，特别是量子物理学，出现了这些设备的功能。以前可以鲁棒地存储信息的系统，当它们被缩小到原子尺度时，就失去了鲁棒地存储信息的能力。另一方面，众所周知，如果人们能够在原子尺度上建造严格按照量子物理定律运行的计算机，那么这些计算机将在今天提供显着的优势？的经典计算机。如果量子计算机能够建造出来，今天就会崩溃吗？的现代密码系统和革命性的模拟量子多体物理。这里提出的研究将产生一种新的方法，用于构建存储和操纵量子信息的鲁棒设备。这种方法首先观察到，经典信息存储是由用于存储信息的设备的物理特性所实现的。例如，用于在硬盘驱动器上存储信息的磁畴是鲁棒的存储设备，这正是因为伊辛模型（二维或更多维）中存在有序的低温相。这里描述的研究遵循了同样的原则，允许强大的经典信息存储：简而言之，研究试图展示如何设计可以作为量子硬盘驱动器的凝聚态系统。这项研究是特别新颖的，因为它与传统的方法直接联系，表明强大的量子计算是可能的，级联编码。在标准纠错中，跨多个独立错误系统对信息进行编码可以降低信息被破坏的速率。通过对编码信息进行编码，也称为连接，可以进一步降低信息破坏率。在这项研究中，这被用于构建一类特殊的多体量子系统，称为量子级联码哈密顿，它使用能量景观的级联思想来保存量子信息。该研究包括一个理论研究验证的强大的存储能力的级联码哈密尔顿沿着一个计划，在各种现实的架构实现themel。这项研究的最终成果将是一种新型量子信息存储设备的原理图，这将大大改善建造量子计算机的前景。

As the basic building blocks of computers shrink to the atomic scale, new physics, in particular quantum physics, arises which shapes how these devices function. Systems that could previously robustly store information, when they are scaled down to atomic scales, lose their ability to robustly store information. On the other hand, it is known that if one could build computers at atomic scales which operate strictly according to the laws of quantum physics, then these computers would offer significant advantages overtoday?s classical computers. Quantum computers, if they could be built, would break today?s modern cryptosystems and revolutionize the simulation of quantum many-body physics. The research proposed here would result in a new method for constructing robust devices for storing and manipulating quantum information. This method starts with the observation that classical information storage is made possible by the physics of the devices used to store the information. For example, the magnetic domains used to store information on a hard drive are robust storage devices exactly because of the existence of an ordered low temperature phase in the Ising model (in two or greater dimensions.) The research described here follows the same principles which allow robust classical storage of information: in short the research attempts to show how toengineer condensed matter systems which can act as a quantum hard drive. Thisresearch is particulary novel in that it makes direct contact with the traditional method for showing that robust quantum computation is possible, concatenated coding. In standard error correction, encoding information across multiple independently erred systems reduces the rate that information is destroyed. By encoding encoded information, also known as concatenating, one can achieve an even further reduction in the rate of information destruction. In this research this is put to use in constructing a particular class of many-body quantum system, called quantum concatenated code Hamiltonians, which use the concatenation idea on energy landscapes to preserve quantum information. The research includes a theoretical study validating the robust storage capability of concatenated code Hamiltonians along a plan for implementing themodel in a variety of realistic architectures. The final outcome of the research will be the schematics for a new type of quantum information storage device, one which will drastically improve the prospects for building a quantum computer.